1. The document provides definitions and concepts related to spur gears, including terms like pitch diameter, diametral pitch, addendum, dedendum, pressure angle, center distance, backlash, gear ratios, and velocity.
2. It explains how to calculate values like pitch diameter, gear tooth dimensions, center distances between gears, and gear ratios. Formulas for determining values like velocity and rotations of gears in a drive system are also presented.
3. The goal is to teach students the terminology and concepts needed to design, draw, build, and discuss gear drive systems so as to improve their "gear literacy."
This document discusses measures of dispersion in statistics. It defines dispersion as the extent of variation in a data set from the average value. There are two main types of dispersion - absolute and relative. Absolute measures express variation in units of the data and include range, variance, standard deviation, and quartile deviation. Relative measures allow comparison between data sets by being unit-free, such as the coefficient of variation. Key absolute measures are then explained in more detail, along with their merits and demerits.
This document contains formulas and definitions for various statistical concepts including measures of central tendency, dispersion, correlation, regression, and time series analysis. It defines formulas for calculating the mean, median, mode, standard deviation, quartiles, correlation coefficients, and linear regression coefficients using both direct and short-cut methods. It also outlines tests for index numbers and methods for weighted aggregation.
Ellipse as an-example-learning-shifts-on-internetDanut Dragoi
The presentation shows an example of learning shifts on the Internet for the ellipse. In a LinkedIn article titled "Learning Shifts on Internet," there are links to the hyperbola, and parabola, which are very useful for teachers and students.
Ellipse as an-example-learning- shifts-on-internet-eraDanut Dragoi
This document discusses the geometry of ellipses using Dandelin spheres. It presents equations to calculate the eccentricity and position of the directrix of an ellipse based on the radii of two imaginary spheres called Dandelin spheres. The document also mentions how this geometric model can be applied to other conic sections like hyperbolas and parabolas. It concludes by noting how the Internet provides helpful resources for fully describing ellipses and other conic sections using synthetic geometry.
The document provides information about spur gear terminology and concepts. It defines key gear terms like pitch diameter, diametral pitch, addendum, dedendum, pressure angle, backlash, gear ratios, and velocity. It explains how to calculate gear dimensions, center distances, gear ratios, and velocity using standard formulas. The objectives are for students to learn how to sketch gear parts, calculate gear dimensions and ratios, and understand how gear drives work.
1. Gears are used to transmit motion between two shafts where slipping needs to be avoided. Gears have teeth cut along the periphery that mesh to ensure positive drive.
2. Gears can be classified based on the position and orientation of shaft axes, peripheral velocity, type of gearing, and position of teeth on the gear surface. Common types include spur gears, helical gears, bevel gears, and rack and pinion.
3. Involute teeth profiles are commonly used as they satisfy the law of gearing to ensure constant velocity ratio between meshing gears for all positions.
The document discusses the synthesis of mechanisms, which involves designing mechanisms to produce desired output motions from given input motions. It covers topics like type synthesis to determine the type of mechanism, number synthesis to determine the number of links and joints, and dimensional synthesis to determine link lengths. It also discusses function generation problems where the output follows a specified function of the input, path generation problems where a point traces a prescribed path, and body guidance problems. Freudenstein's equation for four-bar linkages relating the input and output angles is derived from the kinematic constraints.
The document discusses stress analysis of spur gear teeth and methods to reduce stress using geometric features. It begins with an introduction to gears and gear terminology. It then discusses fatigue failure in gears and how to design against fatigue. The document presents four studies on spur gear models with varying module and number of teeth. The first study analyzes stress variation along the tooth contact path. The second considers actual contact ratio greater than one. The third compares stress for different gear models. The final study selected the weakest gear profile for further stress relief analysis using geometric features like holes. The goal is to investigate how features can reduce stress concentrations and increase gear life.
This document discusses measures of dispersion in statistics. It defines dispersion as the extent of variation in a data set from the average value. There are two main types of dispersion - absolute and relative. Absolute measures express variation in units of the data and include range, variance, standard deviation, and quartile deviation. Relative measures allow comparison between data sets by being unit-free, such as the coefficient of variation. Key absolute measures are then explained in more detail, along with their merits and demerits.
This document contains formulas and definitions for various statistical concepts including measures of central tendency, dispersion, correlation, regression, and time series analysis. It defines formulas for calculating the mean, median, mode, standard deviation, quartiles, correlation coefficients, and linear regression coefficients using both direct and short-cut methods. It also outlines tests for index numbers and methods for weighted aggregation.
Ellipse as an-example-learning-shifts-on-internetDanut Dragoi
The presentation shows an example of learning shifts on the Internet for the ellipse. In a LinkedIn article titled "Learning Shifts on Internet," there are links to the hyperbola, and parabola, which are very useful for teachers and students.
Ellipse as an-example-learning- shifts-on-internet-eraDanut Dragoi
This document discusses the geometry of ellipses using Dandelin spheres. It presents equations to calculate the eccentricity and position of the directrix of an ellipse based on the radii of two imaginary spheres called Dandelin spheres. The document also mentions how this geometric model can be applied to other conic sections like hyperbolas and parabolas. It concludes by noting how the Internet provides helpful resources for fully describing ellipses and other conic sections using synthetic geometry.
The document provides information about spur gear terminology and concepts. It defines key gear terms like pitch diameter, diametral pitch, addendum, dedendum, pressure angle, backlash, gear ratios, and velocity. It explains how to calculate gear dimensions, center distances, gear ratios, and velocity using standard formulas. The objectives are for students to learn how to sketch gear parts, calculate gear dimensions and ratios, and understand how gear drives work.
1. Gears are used to transmit motion between two shafts where slipping needs to be avoided. Gears have teeth cut along the periphery that mesh to ensure positive drive.
2. Gears can be classified based on the position and orientation of shaft axes, peripheral velocity, type of gearing, and position of teeth on the gear surface. Common types include spur gears, helical gears, bevel gears, and rack and pinion.
3. Involute teeth profiles are commonly used as they satisfy the law of gearing to ensure constant velocity ratio between meshing gears for all positions.
The document discusses the synthesis of mechanisms, which involves designing mechanisms to produce desired output motions from given input motions. It covers topics like type synthesis to determine the type of mechanism, number synthesis to determine the number of links and joints, and dimensional synthesis to determine link lengths. It also discusses function generation problems where the output follows a specified function of the input, path generation problems where a point traces a prescribed path, and body guidance problems. Freudenstein's equation for four-bar linkages relating the input and output angles is derived from the kinematic constraints.
The document discusses stress analysis of spur gear teeth and methods to reduce stress using geometric features. It begins with an introduction to gears and gear terminology. It then discusses fatigue failure in gears and how to design against fatigue. The document presents four studies on spur gear models with varying module and number of teeth. The first study analyzes stress variation along the tooth contact path. The second considers actual contact ratio greater than one. The third compares stress for different gear models. The final study selected the weakest gear profile for further stress relief analysis using geometric features like holes. The goal is to investigate how features can reduce stress concentrations and increase gear life.
check it out: http://goo.gl/vqNk7m
CADmantra Technologies pvt. Ltd. is a CAD Training institute specilized in producing quality and high standard education and training. We are providing a perfact institute for the students intersted in CAD courses CADmantra is established by a group of engineers to devlop good training system in the field of CAD/CAM/CAE, these courses are widely accepted worldwide.
#catiatraining
#ANSYS #CRE-O
#hypermesh
#Automobileworkshops
#enginedevelopment
#autocad
#sketching
This document provides a syllabus for a machine drawing course. The syllabus covers topics such as graphic language, orthographic projections, sectional views of machine components, freehand sketching, and assembly drawings. It also discusses principles of machine drawing including lines, scales, dimensioning, tolerances, fits, surface finish, and the representation and terminology of different types of gears like spur gears, helical gears, bevel gears, and worm gears. The syllabus is divided into four sections that cover introduction and principles, orthographic projections and sectional views, freehand sketching, and assembly drawings with sectioning and bills of materials.
A STEM-Maker Level 1 Lesson for System Fluency - Wheel and Axle
What is a Wheel and Axle?
Heavy loads are hard to move by simply pushing
or pulling on them because there are forces that
must be overcome in order for them to move.
One force is gravity, which is the attraction
between the earth and other objects.
This attraction causes the second force known as
friction, which means that the resistance of the
object, as it comes in contact with a surface, must
be overcome before it will move.
The wheel and axle can be used to help move
heavy objects because the surface area of the
wheel is less than the surface area of the load
and this makes it easier to overcome the forces of
gravity and friction.
REVIEW OF TRUE BENDING STRESS IN SPUR GEARIRJET Journal
The document reviews bending stresses in spur gears. It begins by introducing different types of gears and noting that spur gears are commonly used. It then discusses past analytical methods for analyzing gear stresses and notes newer finite element analysis (FEA) methods provide more accurate solutions. The document reviews theories of true bending stress at tooth roots and prior work analyzing stresses through FEA and experimental methods. It concludes the maximum stress occurs at the tooth root and varies with face width.
One of the most important component in mechanical is Gear for the transmission of power with ease and with less friction. Its main aim is to transfer torque from one shaft to other. There are different kinds of gears namely spur gear, helical gears, worm gears etc. Gear drives are used for different kinds of machines like automobiles, metal cutting tools, material handling equipment’s, rolling mills, marine power plants etc. The friction and other losses in this type of power transmission equipment is comparatively very low. In this work a software called “MATLAB†is used to design a Spur Gear. MATLAB is widely used for lot of research purposes for obtaining accurate results and it has got a lot of built in functions which makes it versatile. It is a user friendly one and when executed it ask the inputs and performs the necessary design calculations and gives necessary output values. As computers are used to perform the task of gear design becomes simple, friendly and error free.
The document discusses various terms and measurements related to gear teeth. It defines terms like pitch circle, diametral pitch, module, addendum, dedendum, clearance, pressure angle, and helix angle. It also describes common methods for measuring individual elements of gear teeth, such as tooth thickness, pitch, and errors, using instruments like gear tooth calipers, constant chord method, and base tangent method. Sources of errors in gear manufacturing by generating and reproducing methods are also outlined.
This document provides definitions for common gear terminology used in gear design and calculation. It defines key terms like module, which is the ratio of the pitch diameter to the number of teeth and appears in many gear calculation formulas. It also defines other important terms like reference diameter, center distance, and pressure angle. The reference diameter connects to other parameters and is used in gear ratios to calculate the turning of two engaged gears. Finally, it notes that properly matching gears have the same module and pressure angle.
IRJET- Parametric Stress Analysis of Helical Gear using FeaIRJET Journal
This document analyzes the stresses in a helical gear pair using finite element analysis. It describes creating 3D solid models of helical gears with different modules in SolidWorks. The models are then analyzed in ANSYS to calculate von Mises stresses and contact stresses. Results show that the maximum von Mises stress is around 124 MPa for both modules. The maximum contact stress occurs at the pitch point and increases from root to pitch before decreasing to the tip, due to changes in the load sharing ratio between contacting teeth. Increasing the module and face width reduces maximum contact stress by promoting three-tooth contact over two-tooth contact.
This document summarizes a study on modeling and analyzing an involute helical gear using CATIA and ANSYS software. It begins with an introduction to gears and motivation for using numerical analysis methods. It then describes how a helical gear model was generated in CATIA and its stresses were analyzed using ANSYS. Bending stresses from ANSYS were compared to theoretical Lewis equation values and AGMA standards, showing maximum 1.4% deviation. Face width was varied and stresses decreased with increasing width. Overall, complex gear designs require advanced software for accurate modeling and stress analysis to optimize design and prevent failures.
Finit element in prosthodontics /certified fixed orthodontic courses by India...Indian dental academy
The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and offering a wide range of dental certified courses in different formats.
This document discusses gear measurements and metrology. It defines key gear terminology such as pitch circle, pressure angle, addendum, dedendum, and circular pitch. It then describes methods for measuring gear concentricity using rollers or a projector. Alignment of individual teeth can be analyzed mathematically or through functional testing. Rolling gear tests using a Parkinson gear tester can efficiently measure variations in center distance to identify errors. Individual gear elements like tooth thickness are measured using methods like a gear tooth Vernier caliper or constant chord method.
The document describes the process of reverse engineering and modeling a testing part consisting of a shaft with gears. Key steps included:
1. Measuring the part dimensions and determining gear parameters.
2. Developing a modeling strategy starting with a revolve feature to create the shaft profile, then adding holes, rounds, chamfers and gears.
3. Modeling the gear teeth using involute curves defined by gear standards and patterned axially according to the number of teeth.
4. Completing the part model and measuring properties like volume and mass for later experimental validation.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
This document discusses a finite element analysis of stresses in involute gear teeth. A 2D and 3D finite element model of spur gear teeth were created in ANSYS. Bending and contact stresses were analyzed for different applied torques and material properties. The results from the finite element models were compared to theoretical calculations using AGMA and Hertz contact stress equations. The 2D model was found to provide more accurate stress results than the 3D model, while requiring less computational resources. The type of contact condition modeled was found to significantly impact the stress results.
THE ANALYTICAL STUDY OF MESHING OF DOUBLE HELICAL GEARIJARIIT
The document describes a study analyzing stress in double helical gears using finite element analysis. It discusses previous research on gear stress analysis. The study models two gear stages and performs static structural analysis under specified loads. Results show maximum stress exceeds the material yield strength. The gear geometry is then modified by adding a hole, tapering tooth edges, and adding a groove to reduce stress concentrations. Modified models are re-analyzed to evaluate effect on stress levels.
The document defines key terminology used in spur gear design, including:
- Pitch circle: An imaginary circle that would give the same motion as the actual gear through rolling action.
- Addendum: The distance from the pitch circle to the top of a tooth.
- Dedendum: The distance from the pitch circle to the bottom of a tooth.
- Circular pitch: The distance on the pitch circle between corresponding points on adjacent teeth.
- Pressure angle: The angle between the common normal and common tangent at the point of contact between two meshing gear teeth. Standard pressure angles are 14.5° and 20°.
Finite element modeling and bending stress analysis of non standard spur geareSAT Journals
Abstract Gears are toothed wheels, transmitting power and motion from one shaft to another by means of successive engagement of teeth. Having a higher degree of reliability, compactness, high velocity ratio and finally able to transmit motion at a very low velocity, gears are gaining importance as the most efficient means for transmitting power. A gearing system is susceptible to problems such as interference, backlash and undercut. The contact portions of tooth profiles that are not conjugate is called interference. Furthermore due to interference and in the absence of undercut, the involute tip or face of the driven gear tends to dig out the non-involute flank of the driver. The response of a spur gear and its wear is an engineering problem that has not been completely overcome yet. With the perspective of overcoming such defects and for increase the efficiency of gearing system, the use of a non-standard spur gear i.e., an asymmetric spur gear having different pressure angles for drive and coast side of the tooth comes into picture. This paper emphasis on the generation of an asymmetric spur gear tooth using modeling software and bending stress at the root of Asymmetric spur gear tooth is estimated by finite element analysis using ANSYS software and results were compared with the standard spur gear tooth. Keywords: Asymmetric spur gear, Bending stress, Finite element method, Pressure angle
The document discusses gears and gear trains. It begins with an overview of different types of gears including spur gears, helical gears, bevel gears, and worm gears. It then provides details on gear terminology such as pitch diameter, pitch circle, addendum, and dedendum. The document also discusses how to calculate gear ratios in single and compound gear trains. Design considerations for gear trains including selecting gear tooth counts and sizes to achieve specific gear ratios are also covered.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
check it out: http://goo.gl/vqNk7m
CADmantra Technologies pvt. Ltd. is a CAD Training institute specilized in producing quality and high standard education and training. We are providing a perfact institute for the students intersted in CAD courses CADmantra is established by a group of engineers to devlop good training system in the field of CAD/CAM/CAE, these courses are widely accepted worldwide.
#catiatraining
#ANSYS #CRE-O
#hypermesh
#Automobileworkshops
#enginedevelopment
#autocad
#sketching
This document provides a syllabus for a machine drawing course. The syllabus covers topics such as graphic language, orthographic projections, sectional views of machine components, freehand sketching, and assembly drawings. It also discusses principles of machine drawing including lines, scales, dimensioning, tolerances, fits, surface finish, and the representation and terminology of different types of gears like spur gears, helical gears, bevel gears, and worm gears. The syllabus is divided into four sections that cover introduction and principles, orthographic projections and sectional views, freehand sketching, and assembly drawings with sectioning and bills of materials.
A STEM-Maker Level 1 Lesson for System Fluency - Wheel and Axle
What is a Wheel and Axle?
Heavy loads are hard to move by simply pushing
or pulling on them because there are forces that
must be overcome in order for them to move.
One force is gravity, which is the attraction
between the earth and other objects.
This attraction causes the second force known as
friction, which means that the resistance of the
object, as it comes in contact with a surface, must
be overcome before it will move.
The wheel and axle can be used to help move
heavy objects because the surface area of the
wheel is less than the surface area of the load
and this makes it easier to overcome the forces of
gravity and friction.
REVIEW OF TRUE BENDING STRESS IN SPUR GEARIRJET Journal
The document reviews bending stresses in spur gears. It begins by introducing different types of gears and noting that spur gears are commonly used. It then discusses past analytical methods for analyzing gear stresses and notes newer finite element analysis (FEA) methods provide more accurate solutions. The document reviews theories of true bending stress at tooth roots and prior work analyzing stresses through FEA and experimental methods. It concludes the maximum stress occurs at the tooth root and varies with face width.
One of the most important component in mechanical is Gear for the transmission of power with ease and with less friction. Its main aim is to transfer torque from one shaft to other. There are different kinds of gears namely spur gear, helical gears, worm gears etc. Gear drives are used for different kinds of machines like automobiles, metal cutting tools, material handling equipment’s, rolling mills, marine power plants etc. The friction and other losses in this type of power transmission equipment is comparatively very low. In this work a software called “MATLAB†is used to design a Spur Gear. MATLAB is widely used for lot of research purposes for obtaining accurate results and it has got a lot of built in functions which makes it versatile. It is a user friendly one and when executed it ask the inputs and performs the necessary design calculations and gives necessary output values. As computers are used to perform the task of gear design becomes simple, friendly and error free.
The document discusses various terms and measurements related to gear teeth. It defines terms like pitch circle, diametral pitch, module, addendum, dedendum, clearance, pressure angle, and helix angle. It also describes common methods for measuring individual elements of gear teeth, such as tooth thickness, pitch, and errors, using instruments like gear tooth calipers, constant chord method, and base tangent method. Sources of errors in gear manufacturing by generating and reproducing methods are also outlined.
This document provides definitions for common gear terminology used in gear design and calculation. It defines key terms like module, which is the ratio of the pitch diameter to the number of teeth and appears in many gear calculation formulas. It also defines other important terms like reference diameter, center distance, and pressure angle. The reference diameter connects to other parameters and is used in gear ratios to calculate the turning of two engaged gears. Finally, it notes that properly matching gears have the same module and pressure angle.
IRJET- Parametric Stress Analysis of Helical Gear using FeaIRJET Journal
This document analyzes the stresses in a helical gear pair using finite element analysis. It describes creating 3D solid models of helical gears with different modules in SolidWorks. The models are then analyzed in ANSYS to calculate von Mises stresses and contact stresses. Results show that the maximum von Mises stress is around 124 MPa for both modules. The maximum contact stress occurs at the pitch point and increases from root to pitch before decreasing to the tip, due to changes in the load sharing ratio between contacting teeth. Increasing the module and face width reduces maximum contact stress by promoting three-tooth contact over two-tooth contact.
This document summarizes a study on modeling and analyzing an involute helical gear using CATIA and ANSYS software. It begins with an introduction to gears and motivation for using numerical analysis methods. It then describes how a helical gear model was generated in CATIA and its stresses were analyzed using ANSYS. Bending stresses from ANSYS were compared to theoretical Lewis equation values and AGMA standards, showing maximum 1.4% deviation. Face width was varied and stresses decreased with increasing width. Overall, complex gear designs require advanced software for accurate modeling and stress analysis to optimize design and prevent failures.
Finit element in prosthodontics /certified fixed orthodontic courses by India...Indian dental academy
The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and offering a wide range of dental certified courses in different formats.
This document discusses gear measurements and metrology. It defines key gear terminology such as pitch circle, pressure angle, addendum, dedendum, and circular pitch. It then describes methods for measuring gear concentricity using rollers or a projector. Alignment of individual teeth can be analyzed mathematically or through functional testing. Rolling gear tests using a Parkinson gear tester can efficiently measure variations in center distance to identify errors. Individual gear elements like tooth thickness are measured using methods like a gear tooth Vernier caliper or constant chord method.
The document describes the process of reverse engineering and modeling a testing part consisting of a shaft with gears. Key steps included:
1. Measuring the part dimensions and determining gear parameters.
2. Developing a modeling strategy starting with a revolve feature to create the shaft profile, then adding holes, rounds, chamfers and gears.
3. Modeling the gear teeth using involute curves defined by gear standards and patterned axially according to the number of teeth.
4. Completing the part model and measuring properties like volume and mass for later experimental validation.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
This document discusses a finite element analysis of stresses in involute gear teeth. A 2D and 3D finite element model of spur gear teeth were created in ANSYS. Bending and contact stresses were analyzed for different applied torques and material properties. The results from the finite element models were compared to theoretical calculations using AGMA and Hertz contact stress equations. The 2D model was found to provide more accurate stress results than the 3D model, while requiring less computational resources. The type of contact condition modeled was found to significantly impact the stress results.
THE ANALYTICAL STUDY OF MESHING OF DOUBLE HELICAL GEARIJARIIT
The document describes a study analyzing stress in double helical gears using finite element analysis. It discusses previous research on gear stress analysis. The study models two gear stages and performs static structural analysis under specified loads. Results show maximum stress exceeds the material yield strength. The gear geometry is then modified by adding a hole, tapering tooth edges, and adding a groove to reduce stress concentrations. Modified models are re-analyzed to evaluate effect on stress levels.
The document defines key terminology used in spur gear design, including:
- Pitch circle: An imaginary circle that would give the same motion as the actual gear through rolling action.
- Addendum: The distance from the pitch circle to the top of a tooth.
- Dedendum: The distance from the pitch circle to the bottom of a tooth.
- Circular pitch: The distance on the pitch circle between corresponding points on adjacent teeth.
- Pressure angle: The angle between the common normal and common tangent at the point of contact between two meshing gear teeth. Standard pressure angles are 14.5° and 20°.
Finite element modeling and bending stress analysis of non standard spur geareSAT Journals
Abstract Gears are toothed wheels, transmitting power and motion from one shaft to another by means of successive engagement of teeth. Having a higher degree of reliability, compactness, high velocity ratio and finally able to transmit motion at a very low velocity, gears are gaining importance as the most efficient means for transmitting power. A gearing system is susceptible to problems such as interference, backlash and undercut. The contact portions of tooth profiles that are not conjugate is called interference. Furthermore due to interference and in the absence of undercut, the involute tip or face of the driven gear tends to dig out the non-involute flank of the driver. The response of a spur gear and its wear is an engineering problem that has not been completely overcome yet. With the perspective of overcoming such defects and for increase the efficiency of gearing system, the use of a non-standard spur gear i.e., an asymmetric spur gear having different pressure angles for drive and coast side of the tooth comes into picture. This paper emphasis on the generation of an asymmetric spur gear tooth using modeling software and bending stress at the root of Asymmetric spur gear tooth is estimated by finite element analysis using ANSYS software and results were compared with the standard spur gear tooth. Keywords: Asymmetric spur gear, Bending stress, Finite element method, Pressure angle
The document discusses gears and gear trains. It begins with an overview of different types of gears including spur gears, helical gears, bevel gears, and worm gears. It then provides details on gear terminology such as pitch diameter, pitch circle, addendum, and dedendum. The document also discusses how to calculate gear ratios in single and compound gear trains. Design considerations for gear trains including selecting gear tooth counts and sizes to achieve specific gear ratios are also covered.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024Sinan KOZAK
Sinan from the Delivery Hero mobile infrastructure engineering team shares a deep dive into performance acceleration with Gradle build cache optimizations. Sinan shares their journey into solving complex build-cache problems that affect Gradle builds. By understanding the challenges and solutions found in our journey, we aim to demonstrate the possibilities for faster builds. The case study reveals how overlapping outputs and cache misconfigurations led to significant increases in build times, especially as the project scaled up with numerous modules using Paparazzi tests. The journey from diagnosing to defeating cache issues offers invaluable lessons on maintaining cache integrity without sacrificing functionality.
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
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6.3.1 gear terms_lesson_rev3
1. 1
GEARS Educational Systems 105 Webster St. Hanover Massachusetts 02339 Tel. 781 878 1512 Fax 781 878 6708 www.gearseds.com
Spur Gear Terms and Concepts
Description
In order to design, build and discuss gear drive systems it is necessary to understand the terminology and
concepts associated with gear systems. Good designers and engineers have experience and knowledge and
the ability to communicate their thoughts and ideas clearly with others. The students and teachers who
participate in this unit will learn the gear terms and concepts necessary to design, draw and build gear
drive systems, and improve their “Gear literacy”.
Standards Addressed
National Council of Teachers of English Standards (http://www.readwritethink.org/standards/index.html )
• Students adjust their use of spoken, written, and visual language (e.g., conventions, style,
vocabulary) to communicate effectively with a variety of audiences and for different purposes.
• Students conduct research on issues and interests by generating ideas and questions, and by
posing problems. They gather, evaluate, and synthesize data from a variety of sources (e.g., print
and non-print texts, artifacts, people) to communicate their discoveries in ways that suit their
purpose and audience.
• Students participate as knowledgeable, reflective, creative, and critical members of a variety of
literacy communities.
• Students use spoken, written, and visual language to accomplish their own purposes (e.g., for
learning, enjoyment, persuasion, and the exchange of information).
National Council of Mathematics Teachers
( 9-12 Geometry Standards) ( http://standards.nctm.org/document/appendix/geom.htm )
• Analyze properties and determine attributes of two- and three-dimensional objects
• Explore relationships (including congruence and similarity) among classes of two- and three-
dimensional geometric objects, make and test conjectures about them, and solve problems
involving them;
(9-12 Algebra Standards) http://standards.nctm.org/document/chapter7/alg.htm
• Understand and perform transformations such as arithmetically combining, composing, and
inverting commonly used functions, using technology to perform such operations on more-
complicated symbolic expressions.
• Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations
• Use symbolic algebra to represent and explain mathematical relationships;
(9-12 ) Science and Technology Standards (from the National Science Standards web page)
http://www.nap.edu/readingroom/books/nses/html/6a.html#unifying
• The abilities of design. Using math to understand and design gear forms is an example of one
aspect of an ability to design.
105 Webster St. Hanover Massachusetts 02339 Tel. 781 878 1512 Fax 781 878 6708 www.gearseds.com
2. 2
GEARS Educational Systems 105 Webster St. Hanover Massachusetts 02339 Tel. 781 878 1512 Fax 781 878 6708 www.gearseds.com
Terms
Active Profile
Addendum
Backlash
Base Circle
Center Distance
Chordal Thickness
Circular Pitch
Circular Thickness
Dedendum
Diametral Pitch
Gear Ratios
Herringbone Gears
Idler Gear
Involute
Module
Pitch
Pitch Diameter
Pitch Point
Pressure Angle
Profile
Rack
Spur Gear
Velocity
Whole Depth
Working Depth
Materials/Equipment/Supplies/Software
Pencils
8-1/2 x 11” Paper
Compass
Protractor
Ruler
Straight Edge
1-2’ String
Tin Can
Tape
GEARS-IDS Kit
GEARS-IDS Optional Gear Set
Objectives.
Students who participate in this unit will:
1. Sketch and illustrate the parts of a spur gear.
2. Calculate gear and gear tooth dimensions using gear pitch and the number of teeth.
3. Calculate center to center distances for 2 or more gears in mesh.
4. Calculate and specify gear ratios.
Some Things to Know Before You Start
How to use a compass
How to use a protractor to measure angles
How to solve simple algebraic expression.
Basic Geometric Terms
3. 3
GEARS Educational Systems 105 Webster St. Hanover Massachusetts 02339 Tel. 781 878 1512 Fax 781 878 6708 www.gearseds.com
Gear Terms and Types
Spur gears have been used since ancient times. Figure
6.3.1.1 shows an illustration of the two-man drive
system that Leonardo Davinci designed to power a his
vision of a helicopter like device. The device never flew,
but the gear system works.
Modern gears are a refinement of the wheel and axle.
Gear wheels have projections called teeth that are
designed to intersect the teeth of another gear. When
gear
teeth fit
together
or
interlock in this manner they are said to be in
mesh. Gears in mesh are capable of transmitting
force and motion alternately from one gear to
another. The gear transmitting the force or motion
is called the drive gear and the gear connected to
the drive gear is called the driven gear.
Gears are Used to Control Power Transmission in These Ways
1. Changing the direction through which power is transmitted (i.e. parallel, right angles,
rotating, linear etc.)
2. Changing the amount of force or torque
3. Changing RPM
Fig. 6.3.1.1 Model of Davinci’s Helicopter Gear
Fig. 6.3.1.2 GEARS-IDS Gear Drive system
4. 4
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Gear Terms, Concepts and Definitions
Spur Gears
Are cogged wheels whose cogs or teeth project radially and stand parallel to the axis.
Diametral Pitch (DP)
The Diametral Pitch describes the gear tooth size. The Diametral Pitch is expressed as the
number of teeth per inch of Pitch Diameter. Larger gears have fewer teeth per inch of
Diametral Pitch. Another way of saying this; Gear teeth size varies inversely with Diametral
Pitch.
Pitch Diameter (D)
The Pitch Diameter refers to the diameter of the pitch
circle. If the gear pitch is known then the Pitch Diameter
is easily calculated using the following formula;
P
N
PD =
Using the values from fig. 6.3.1.3 we find
"5.1
24
36
P
N
PD ===
The Pitch Diameter is used to generate the Pitch Circle.
Fig. 6.3.1.3 DP = #Teeth/Pitch Diameter = 36/1.5 = 24
Fig. 6.3.1.4 Relative Sizes of Diametral Pitch
PD = Pitch Diameter
N = Number of teeth on the gear
P = Diametral Pitch (Gear Size)
5. 5
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The Pitch Circle
The pitch circle is the geometrical starting point for designing gears and gear trains. Gear trains
refer to systems of two or more meshing gears. The pitch circle is an imaginary circle that
contacts the pitch circle of any other gear with which it is in mesh. See fig. 6.3.1.5 below.
The pitch circle centers are used to ensure accurate
center-to-center spacing of meshing gears. The
following example explains how the center
distances of meshing gears is determined using the
pitch circle geometry.
Example 6.3.1.1
Calculate the center-to-center spacing for the 2
gears specified below.
Gears: Gear #1) 36 tooth, 24 Pitch Drive Gear
Gear# 2) 60 tooth, 24 Pitch Driven Gear
Step 1.) Calculate the Pitch Diameter for each of the two gears listed above.
Pitch Diameter (D) of gear #1 is: "5.1
24
36
===
P
N
D Pitch Dia. = 1.5”
Pitch Diameter (d) of gear#2 is: "5.2
24
60
===
P
N
D Pitch Dia. = 2.5”
Step 2.) Add the two diameters and divide by 2.
Pitch Dia. of gear #1 = 1.5”
Pitch Dia. Of gear #2 = + 2.5”
Sum of both gear diameters = 4.0”
Divide by 2 Sum of both gear diameters = 4.0”/2 = center to center distance = 2”
(This is necessary since the gear centers are separated by a distance equal to the sum of their
respective radii.)
A simple formula for calculating the center-to-center distances of two gears can be written;
Center-to-Center Distance =
2
21 DD +
Fig. 6.3.1.5 illustrates this relationship.
Fig. 6.3.1.5 Pitch Circle and Gear Teeth in Mesh
6. 6
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Term Definition Calculation
Pitch Diameter (D) The diameter of the Pitch Circle from
which the gear is designed. An imaginary
circle, which will contact the pitch circle of
another gear when in mesh.
P
N
D =
Diametral Pitch (P) A ratio of the number of teeth per inch of
pitch diameter
D
N
P =
Addendum (A) The radial distance from the pitch circle to
the top of the gear tooth
P
A
1
=
Dedendum (B) The radial distance from the pitch circle to
the bottom of the tooth
P
B
157.1
=
Outside Diameter (OD) The overall diameter of the gear
P
N
OD
2+
=
Root Diameter (RD) The diameter at the Bottom of the tooth
P
N
RD
2−
=
Base Circle (BC) The circle used to form the involute section
of the gear tooth
BC = D * Cos PA
Circular Pitch (CP) The measured distance along the
circumference of the Pitch Diameter from
the point of one tooth to the corresponding
point on an adjacent tooth.
PN
D
CP
1416.31416.3
==
Circular Thickness (T) Thickness of a tooth measure along the
circumference of the Pitch Circle
PN
D
T
57.1
2
1416.3
==
Fig. 6.3.1.5a Gear Terms Illustrated
Fig. 6.3.1.5b Key Dimensions for Gear Design
7. 7
GEARS Educational Systems 105 Webster St. Hanover Massachusetts 02339 Tel. 781 878 1512 Fax 781 878 6708 www.gearseds.com
Addendum (A)
The addendum refers to the distance
from the top of the tooth to the Pitch
circle
Dedendum (B)
The Dedendum refers to the distance
from the Pitch circle to the root
circle.
Clearance (C)
Refers to the radial distance between
the top and bottom of gears in mesh.
Some machinists and mechanics
refer to clearance as “play” or the
degree of looseness between mating
parts.
Whole Depth (WD)
Refers to the distance from the top of the tooth to the bottom of the tooth. The whole depth is
calculated using this formula:
P
WD
157.2
=
Pressure Angle (PA) (Choose either 14.5 or 20 degrees)
The pressure angle figures into the geometry or form of the gear tooth. It refers to the angle
through which forces are transmitted between meshing gears.
14.5-degree tooth forms were the original “standard” gear design. While they are still widely
available, the 20-degree PA gear tooth forms have wider bases and can transmit greater loads.
Note: 14.5-degree PA tooth forms will not mesh with 20-degree PA teeth. Be certain to verify the
Pressure angle of the gears you use
Center Distance
The center distance of 2 spur gears is the distance from the center shaft of one spur gear to the
center shaft of the other. Center to center distance for two gears in mesh can be calculated with
this formula. Center-to-Center Distance
2
gearBgearA PDPD +
=
Rotation
Spur gears in a 2-gear drive system (Gear #1 and Gear #2)
will rotate in opposite directions. When an intermediary
gear set or idler gear is introduced between the two gears
the drive gear (Gear #1) and the last gear (Gear #3) will
rotate in the same direction.
Fig. 6.3.1.6 Illustration of Center to Center Distance of Gears in Mesh
8. 8
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The rotational relationship
between gears in a gear drive
system can be stated as follows:
Two meshing gears or gear sets
(Gear sets are comprised of 2 or
more gears fixed to the same
shaft) rotate in opposite
directions. Each odd numbered
gear in a gear drive rotates in the
same direction.
Backlash
Backlash refers to the distance
from the back of the drive gear
tooth to the front of driven gear
tooth of gears mated on the
pitch circle. Standard gears are
designed with a specified amount of backlash to prevent noise and excessive friction and heating
of the gear teeth. (See fig 6.3.1.8)
Fig. 6.3.1.7b Rotation of Three Gear Drive
Fig. 6.3.1.7a Rotation of Two Gear Drive
9. 9
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Ratios
Gears of the same pitch, but differing numbers of teeth can be paired to obtain a wide range of
Gear Ratios. Gear Ratios are used to increase mechanical advantage (torque) or increase
rotational speed or velocity.
The ratio of a given pair of spur gears is calculated by dividing the number of teeth on the driven
gear, by the number of teeth on the drive gear.
The gear ratio in fig. 6.3.1.9 shows a 36 tooth gear driving a 60 tooth gear. The gear ratio can be
calculated as follows;
eethDriveGearT
TeethDrivenGear
GearRation =
1:6.1
36
60
==GearRatio
The ratio describes the drive gear
revolutions needed to turn the driven
gear 1 complete revolution.
Fig. 6.3.1.9 “Low” Gearing to increase torque
Fig. 6.3.1.8 Backlash and Pressure Angle Illustrated
10. 10
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The 1.6:1 gear ratio increases
the torque on the shaft of the
large gear by 1.6X but reduces
the Velocity or RPM of the
large gear shaft by the same
amount
The gear ratio in fig. 6.3.1.10.
shows a 60 tooth gear driving a
36 tooth gear. The gear ratio is
calculated the same as in the
example above.
eethDriveGearT
TeethDrivenGear
GearRation =
67.1:11:6.0
60
36
GearRatio ===
Velocity
Velocity refers to the rotational speed of a gear and can be expressed using a variety of units. In
the examples that follow we will express gear velocity in inches per minute. The gear industry
often uses feet per minute. Inches per minute can be converted to feet per minute by simply
dividing by 12.
Velocity is expressed as the distance a point along the circumference of the pitch circle will
travel over a given unit of time.
Velocity can be calculated using this formula
Velocity = Pitch Circle Circumference x RPM
Example
The 24 pitch drive gear in fig 6.3.1.10 is turning at 100 rpm. What is the velocity of the drive
gear?
Step 1.) Determine the Pitch Diameter (D) "5.2
24
60#
====
P
N
Pitch
Teeth
D
Step 2.) Determine the circumference of the Pitch Circle using the Pitch Diameter.
"854.7"5.21416.3 =∗=∗= DnceCircumfere π
Step 3.) Calculate the gear velocity using the gear velocity formula.
Velocity = 7.854” x RPM = 785.4 inches per minute or 65.45 ft per second.
Fig. 6.3.1.10 “High” Gearing to increase Driven Gear Velocity
11. 11
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Calculate the Velocity of the Driven Gear in the Example Above
The 36 tooth driven gear in the example above is being driven by a larger 60 tooth drive gear. In
order to calculate the driven gear velocity we must first calculate the driven gear RPM using the
gear ratio.
Step 1.) Determine the driven gear RPM using the gear ratio.
Driven Gear RPM = Drive Gear RPM x ratio = 100 x 1.66 = 166 RPM
Step 2.) Determine the Pitch Diameter (D) "5.1
24
36#
====
P
N
Pitch
Teeth
D
Step 3.) Determine the circumference of the Pitch Circle using the Pitch Diameter.
"7124.4"5.11416.3 =∗=∗= DnceCircumfere π
Step 4.) Calculate the gear velocity using the gear velocity formula.
Velocity = 4.7124” x 166 RPM = 782.25 inches per minute or 65.188 ft per
second.
Compare the Velocity in feet per second of the two gears. The velocity of the 60-tooth drive
gear is 65 ft. per minute, AND the velocity of the 36-tooth driven gear is 65 feet per minute.
Gears in mesh rotate at different RPM but always at the same velocity. If this were not true,
then the teeth of the gears would strip off!
Calculating Ratios For Gear Trains with Multiple Gears
The preceding gear ratio problems dealt with two gears, or two gears and an Idler gear. An Idler
gear does not affect the overall ratio between the two adjacent gears. The Idler gear merely
changes the direction of the driven
gear. We can however use
compound gears to create
multiplicative gear ratios that can
dramatically increase torque or
RPM.
In the example on the left, the ratio
between the Drive Gear #1 and the
Driven Gear #3 is 1:1. Both gears
have the same number of teeth
(60T). The Idler Gear #2 simply
transmits the force from the Drive
Gear #1 to the Driven Gear #2.Fig. 6.3.1.11 The Idler Gear changes the Direction
of the Driven Gear
12. 12
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Calculating Ratios for Compound Gear Drives
Let’s look at an example of a multiplicative gear reduction using a compound gear. A compound
gear is made up of two gears solidly connected. Often they are machined from the same stock or
keyed to the same shaft.
The red gear on the left is the drive
gear. This gear can also be called a
pinion gear.
All the gears are rigidly fixed to
the shafts. The green and red
center gears form a compound
gear.
The red drive gear spins at 100
RPM, and drives the 60 tooth
green gear.
The ratio between the red (drive)
gear and the green (driven) gear is
36T:60T or 1.6:1.
Since the green and red gears are affixed to the same shaft, they must both have the same RPM.
We can determine the RPM of the center shaft using the ratio between the red (drive) gear and
the green (driven) gear. As noted previously the ratio is 1.6:1. Thus every time the red (drive)
gear turns 1.6 revolutions, the green (driven) gear turns 1 revolution.
We find the RPM of the green (driven) gear by dividing 100 RPM/1.6 = 62.5 RPM.
Both the red and green center gears are turning at 62.5 RPM. The red center gear now drives the
blue gear on the right.
The ratio between the red center gear and the blue gear is also 36T : 60T or 1.6:1.
We find the RPM of the blue (driven) gear by dividing 62.5 RPM/1.6 = 39.06 RPM.
The overall gear reduction is 100 RPM/39.06 RPM = 2.56:1
Note that if we MULTIPLY the two gear reductions, 1.6 x 1.6 = 2.56
Thus we can calculate the overall gear ration for gear trains with multiple gears by
MULTIPLYING the individual gear reductions.
Fig. 6.3.1.12 Click the Image to View a Movie
13. 13
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Try this gear problem. A 12 tooth gear drives a 48 tooth gear fixed to the center shaft. A 12T
gear is fixed to the same center shaft. The 12T gear on the center shaft drives the blue 60 tooth
gear. If the first gear in the train is rotating at 500 RPM, what is the RPM of the last gear?
Here is a different problem. Assume the 60T gear is the drive gear. It rotates at 500 RPM. What
would the RPM of the the final gear be?
Calculating Torque in Gear Drives
Torque is a measure of the turning or twisting force that acts on axles, gears and shafts. Torque is
proportional to the gear ratio.
This means that in a gear drive system with a 2.67:1 ratio, the torque transmitted from the drive
gear to the driven gear is multiplied 2.67 times.
Assume that a gear of 36 teeth is driving a gear with 96 teeth. A ratio of 2.67:1 is produced.
The torque applied to the shaft of the driven gear is multiplied by 2.67.
Conversely if a gear of 96 teeth is driving a gear with 36 teeth a ratio of 1:2.67 is produced. The
torque applied to the shaft of the driven gear will be reduced or divided by 2.67.
12T
48T
12T
60T
500 RPM
Fig. 6.3.1.13 Compound Gear Drive
14. 14
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Looking at this mathematically we can say that a Ratio of 2.67:1 is equivilant to the fraction
1
67.2
in order to find the torque multiple created by this ratio, simply multiply the drive
gear torque by 1
67.2
.
On the other hand a Ratio of 1:2.67 is equivilant to the fraction
67.2
1
. To find the torque
created by this ratio, simply multiply the drive gear torque by
67.2
1
Calculate the Transmitted Torques
The drive gear torque is 3 ft. lbs.
Step 1.) Calculate the gear ratio. 1:67.2
36
96
DriveGear
DrivenGear
Ratio ===
Step 2.) Multiply torque by the gear ratio = *
1
67.2
3 ft.lbs = 8 ft. lbs. Torque
Fig. 6.3.1.14
15. 15
GEARS Educational Systems 105 Webster St. Hanover Massachusetts 02339 Tel. 781 878 1512 Fax 781 878 6708 www.gearseds.com
Activities
Activity #1
Use the information in this lesson to make a careful, full sized sketch of a 8 pitch gear having 24
teeth. Use a compass, protractor, dividers, ruler and a straight edge. Accurately draw and label
the following gear geometry.
Pitch Diameter
Diametral Pitch (Pitch)
Whole Depth
Root Diameter
Pitch Circle
Number of Teeth
Pressure Angle
Circular Thickness
Addendum (Numerical
Value)
Dedendum
Circular Pitch
Activity #2
The curved section of a gear tooth is called an involute curvature. An involute can be created by
wrapping a string around a cylinder and tying a pencil on the free end. Use an 18” string, a pencil
and a tin can to create involute designs on a piece of paper. Keep the paper in your notebook.
Print your name, and the date you completed this assignment on the top of the page.
Activity #3
Download the GEARS-IDS Activity_document_6.3.1_Assemble Gear_drive.pdf. Use the
GEARS-IDS components and the instructions provided in this manual to construct a mobile
robot chassis powered by an electric motor and a gear drive. This mobile chassis can be used for
experiments associated with torque, velocity, robot control and more.
Note: This activity requires the GEARS-IDS optional Gear Set. Call 781-878-1512 to order the
optional gear set. It is possible to construct this gear drive module with standard gears that can be
obtained from a variety of sources.
Activity#4
Choose a gear drive related topic and independently prepare a 4-8 slide presentation that shares
the knowledge and information you have gained through your research. Use graphics that you
create in CAD, Photoshop, Power Point, etc. The expectation is that the presentation will be
informative and interesting for the audience.
Activity#5
Create a spreadsheet program that can solve for 5 or more of the following gear values:
Pitch Diameter
Pitch Circle Circumference
Diametral Pitch
Addendum
Base Circle
Dedendum
Whole Depth
Outside Diameter
Root Diameter
Circular Pitch
Velocity of Driven Gear
Velocity of Drive Gear
Gear Ratios
16. 16
GEARS Educational Systems 105 Webster St. Hanover Massachusetts 02339 Tel. 781 878 1512 Fax 781 878 6708 www.gearseds.com
Worksheets.
Refer to Worksheet 6.3.1.1
Links and Resources.
http://auto.howstuffworks.com/gear1.htm A well written and beautifully presented gear
resource.
http://stellar.mit.edu/SRSS/rss/course/2/sp09/2.007/ Slide shows about screws and gears. These
documents are available through the Mechanical Engineering department at MIT. “Gifts” like
these are available from many different universities.
http://stellar.mit.edu/S/course/2/sp09/2.007/ This link is to the front page of the MIT 2.007 Design and
Manufacturing course….the grand daddy of all the robot and engineering games we hear about
today!
Rubric and Assessment
Rubrics define the levels of proficiency and achievement and describe what the student should
know and be able to do as a result of participating in the lesson or activity.
The matrix on the following page is offered as an example of a Rubric written to reflect the
objectives, standards and activities that are directly related to this Spur Gear lesson. Teachers are
encouraged to modify this assessment tool to reflect the focus and activities they choose to
include with this unit.
17. 17
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Proficiency Meets/Exceeds
Requirement
Meets Some of the
Requirement
Meets little or None
of the Requirement
Demonstrates a working
knowledge of gear
terminology through spoken,
written and visual language
Researches information
about gear drives and
generates ideas and
questions by posing
problems
Gathers, evaluates, and
synthesizes data from a
variety of sources (e.g., print
and non-print texts, artifacts,
people) to communicate their
understanding of Gear drives
Presents clear and accurate
sketches that detail and
illustrate all the
nomenclature associated
with spur gears
Calculates the key
dimensions associated with
gear design (Fig. 6.3.1.5b)
Calculates and specify gear
ratios
Completes a working model
of a gear drive and uses it to
power a mechanism.
Creates a design(s) using
involute curves.
Creates spreadsheet
solutions for commonly used
formulas
Uses equivalent expressions
to solve gear problems
Assessment Rubric for Spur Gear Terms and Concepts
18. 18
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Additional Assessment Tools Include:
Performance assessment.
Portfolio (An organized chronology of individual achievement. This could be a notebook
or a web page or a multimedia presentation)
Work Sheets, Labs and design challenges.
Examples of Spread Sheets to Solve Gear Related Problems
Tests and Quizzes
Student Response/Journal Entry/Assignments
This is a listing of required documents or deliverables to be produced and present in each
student’s notebook.
1. Gear Sketches
2. Work Sheet
3. Research Presentation
4. Involute
5. Tests or Quizzes.
Media Content.
Slide Presentations
19. 19
GEARS Educational Systems 105 Webster St. Hanover Massachusetts 02339 Tel. 781 878 1512 Fax 781 878 6708 www.gearseds.com
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